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Conditions for Bubble Formation

in

Porous Regions and Narrow Channels

Craig E. Nelson - Consultant Engineer

Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com

Homogeneous nucleation is bubble nucleation without use of a nucleation site

Heterogeneous nucleation is bubble nucleation at a nucleation site

Nucleation sites are typically small dust particles or crevices in a wall

Homogeneous nucleation does not occur as easily as Heterogeneous nucleation

This means that if homogeneous nucleation can occur, bubbles will form

Therefore:

The following analysis is concerned with homogeneous nucleation only.

Note:

In unusual circumstances, bubbles do not form as predicted by the following analysis.The liquid then becomes supersaturated. A supersaturated liquid may spontaneously“boil” in a violent manner. Any small disturbance of the liquid can set this off.

The Two kinds of Bubble Nucleation

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Critical Diameter

There is a critical diameter for bubbles in a liquid

If the bubble is larger than the critical diameter, it will grow in size until buoyantand-or other forces carry it away

If the bubble is smaller than the critical diameter, it will shrink in size until is hasbeen completely dissolved or contaminants in the liquid prevent it from shrinkingaway completely

The critical diameter is determined by the balance of three forces: Force 1 = Ambient pressure … causes shrinking Force 2 = Surface tension (Young-Laplace force) … causes shrinking Force 3 = Chemical pressure (Henry’s Law force) … causes expansion

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Force Balance

Pambient = 10^5 Pascals - STP

Young-Laplace = 2 * surface Tension / Bubble Radius

Henry’s Law =

i

K henry i * Concentration i

Bubbles will not form if :

i

K henry i * Concentration i Pambient + 2 * surface Tension / Bubble Radius<

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Max Pore Size that Prevents Homo-Nucleation

To prevent homogeneous nucleation, the maximum pore size that a chance collection ofsmall colliding bubbles could grow too must be less than the critical bubble diameter.

When the pore diameter is less than the critical bubble diameter, even if a bubble grows to thefull diameter of the pore that it forms within, it will quickly-spontaneously shrink and dissolveback into the liquid from which it emerged.

When the pore diameter is greater than the critical diameter, when a bubble grows to thefull diameter of the pore that it forms within, It will stay there and block that region thereafter.

Alternatively, the bubble may leave its pore region of origin and move a small distance towarda narrow passageway … where it might get permanently stuck.

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Critical Diameter – 1 M CO2 in H20 at STP

Young-Laplace and Chemical Pressure - CO2

1.00E+05

1.00E+061.00E+07

1.00E+081.00E+09

1.00E+10

0.0001 0.01 1 100 10000

Pore Diameter (microns)

Pres

sure

(Pa)

Chem Pressure

Laplace Pressure

.1 microns100 nanometers

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Critical Diameter – 1 M NO2 in H20 at STP

Young-Laplace and Chemical Pressure - NO2

1.00E+051.00E+061.00E+07

1.00E+081.00E+091.00E+10

0.0001 0.01 1 100 10000

Pore Diameter (microns)

Pres

sure

(Pa) Chem Pressure

Laplace Pressure

.05 microns50 nanometers

Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com

Critical Diameter – 1 M NO in H20 at STP

Young-Laplace and Chemical Pressure - NO

1.00E+051.00E+061.00E+07

1.00E+081.00E+091.00E+10

0.0001 0.01 1 100 10000

Pore Diameter (microns)

Pres

sure

(Pa) Chem Pressure

Laplace Pressure

.005 microns5 nanometers

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Summary

If you can’t prevent homogeneous bubble nucleation, you are going to have bubbles

Pores that are small enough will prevent homogeneous bubble nucleation

Supersaturated gas-liquid solutions will form bubbles if pore size increases abovethe critical diameter. Calculated critical diameters for 1 M concentrations at STPare: CO2 < 100 nanometers NO2 < 50 nanometers NO < 5 nanometers